The invention relates to a lens arrangement for the focusing of a beam of electrically charged particles in the beam path of imaging systems, more particularly in mass spectrometers for the examination of organic and inorganic substances, the lens arrangement is being connected to an electrical voltage supply. The invention further relates to a double-focus mass spectrometer, having an ion source, having an imaging system, consisting of a sector field magnet, an electrostatic analyser and other ion-optical elements in any sequence, and having a detector, positioned behind, for the particles of organic and inorganic substances to be examined.
With imaging systems for electrically charged particles, more particularly with double-focus mass spectrometers of the initially mentioned type, focusing problems arise in practice in circumstances in which it is desired to permit large aperture angles, large beam heights or large energy bandwidths in the electrically charged particle beam. This is because a part is played in these circumstances not only by the image defects of the first order, but also by the image defects of the second order, which are then no longer negligible. In these cases, both second order directional focusing and also second order energy focusing should accordingly be undertaken, in order that the mass resolution should not be impaired by image defects of the second order.
There are indeed analysers in such imaging systems, which permit a double focus of the second order, but the previously known special embodiments in practice involve certain disadvantages. For example, at a given radius of the sector field magnet, a very large electrostatic analyser must be used, so that overall large dimensions, a large magnet deflection angle and thus a costly magnet are required. Frequently, in such an arrangement only focusing in an axial direction of a coordinate system is possible, while focusing in the axial direction perpendicular thereto is not possible.
In order to explain the problem, the situation is first to be explained in general terms with reference to FIG. 6 of the drawing. An important quality feature of a mass spectrometer is its mass resolution, which is given by the following formula: ##EQU1## where the following symbols have been employed: A.sub.65 =mass dispersion coefficient
A.sub.x =Image magnification in the x direction PA1 S=Width of the entrance gap in the x direction PA1 .DELTA.=Aberration in consequence of all image defects which are present. PA1 x.sub.0 =half-width of the object gap PA1 y.sub.0 =half-height of the object gap PA1 .alpha..sub.0 =half aperture angle in the x direction (in the deflection plane) PA1 .beta..sub.0 =half aperture angle in the y direction PA1 .delta..sub.0 =energy deviation with .delta..sub.0 =E/E PA1 .gamma..sub.0 =mass deviation with, .gamma..sub.0 =m/m.
In this arrangement, as is represented FIG. 6, x is the horizontal coordinate, which lies in the deflection direction.
As beam axis there is designated the path of a so-called reference particle, which possesses the desired mass and energy. The coordinate system is set in the path of this reference particle. Accordingly, the reference particle has at the entrance gap the initial coordinates: EQU x.sub.0 =y.sub.0 =.alpha..sub.0 =.beta..sub.0 =.delta..sub.0 =0
and at the exit gap the final coordinates: EQU x.sub.1 =y.sub.1 =.alpha..sub.1 =.beta..sub.1 =.delta..sub.1 =.gamma..sub.1 =0.
In these equations, as is evident from FIG. 6, the symbols used hereinabove have the following meanings:
A charged particle, e.g. an ion, which enters the deflection system or the mass spectrometer from the entrance gap with specific initial coordinates (designated by the subscript 0) arrives at the exit gap with specific final coordinates (designated by the subscript 1). In this connection, the quantity of predominant interest is the final coordinate x.sub.1, since this deviation in the x direction has a direct effect on the mass resolution. The final coordinate x.sub.1 may be described by the following equation: ##EQU2##
The various image defect coefficients are designated by the letter A and the corresponding subscript in these equations. In the formula for the mass resolution set forth hereinabove, the expression for X.sub.1 corresponds to the term, designated by .DELTA., for the aberration.
In a double focus mass spectrometer, there is a first order directional and energy focusing, so that the deflect coefficients are A.sub..alpha. =A.sub.67 =0.
A.sub.x is the magnification in the x direction, which is of the order of magnitude of one if the geometrical arrangements of the imaging system are normal.
A.sub..gamma. relates to the mass dispersion, which is desired in order to be able to separate differing masses.
The remaining indicated coefficients are second order image defect coefficients. Thus, in order to achieve the desired second order double focus, it is necessary in the imaging system to bring both the coefficient A.sub..alpha..alpha. for the directional focusing and also the coefficients A.sub..alpha..delta. and A.sub..delta..delta. for the energy focusing to the value 0, or at least to make them negligibly small.